Separate in two parts a Mesh using Knife Project
After further research, I have decided to scrap everything that I had before (it isn't that complicated). You can see my edits if you'd like to see the &quot;old&quot; way.
1. Select all vertices
This is pretty self-explanatory. Make sure you're in edit mode, then hit A
2. Use the Bisect tool
Just drag and you should get a live display of where it will cut. (You can alternatively use the plane and knife project at this stage if you'd prefer. Just make sure to enable &quot;cut through.&quot;) When you are done with Bisect or Knife Project, you should have the &quot;cut&quot; selected.
3. Rip/Tear the selected (&quot;cut&quot;) vertices
For this step, hit V, then left-click before moving the mouse. This essentially makes a nice set of double vertices on the edge of the cut.
4. Select the top or bottom
Deselect all, then you can use the L select linked tool on the top or bottom. Make sure you get everything in the top including the half of the cut line.
5. Separate the mesh
Use P + Selection to quickly separate.

Here is the complete GIF (I finished the operation in 30 seconds):